Vector Calculus: Plotting Tangent Surface

Plotting a tange

library(plotly)
library(pracma)
library(Deriv)
plot_tangent_surface = function(f, x_0, y_0, grid_x = -10, grid_y = 10) {
  # Create meshgrid for plotting 
  m = meshgrid(grid_x:grid_y)
  nrows = nrow(m$X)
  X = as.vector(m$X)
  Y = as.vector(m$Y)
  z_0 = f(x_0, y_0)
  df_dx = Deriv(f, 'x')
  df_dy = Deriv(f, 'y')
  
  F_MAT = f(X, Y)
  SURFACE = z_0 + df_dx(x_0, y_0)*(X - x_0) + df_dy(x_0, y_0)*(Y - y_0)
  
  F_MAT = matrix(F_MAT, nrow = nrows)
  SURFACE = matrix(SURFACE, nrow = nrows)
  
  p <- plot_ly(z = ~F_MAT) %>% add_surface(
    contours = list(
        z = list(
        show=TRUE,
        usecolormap=TRUE,
        highlightcolor="#ff0000",
        project=list(z=TRUE)
      )
    )
  ) %>%
    layout(
      scene = list(
        camera=list(
          eye = list(x=1.87, y=0.88, z=-0.64)
        )
      )
    ) %>%
    add_surface(z = ~SURFACE)
  
  p
}
# Define f
f = function(x, y) {
  x^2  + y^2
}
x_0 = -3
y_0 = -3
# debug(plot_tangent_surface)
plot_tangent_surface(f, x_0, y_0, -15, 15)